MathDB

Let

ABCD

be a cyclic quadrilateral,

O

be its circumcenter,

P

be a common points of its diagonals, and

M , N

be the midpoints of

AB

and

CD

respectively. A circle

OPM

meets for the second time segments

AP

and

BP

at points

A_1

and

B_1

respectively and a circle

OPN

meets for the second time segments

CP

and

DP

at points

C_1

and

D_1

respectively. Prove that the areas of quadrilaterals

AA_1B_1B

and

CC_1D_1D

are equal.

Problem Statement